BSDEs and SDEs with time-advanced and -delayed coefficients. Issue 6 (18th August 2019)

• Record Type: Journal Article
• Authors: Zheng, Shiqiu; Zong, Gaofeng
• Is Part Of: Stochastics. Volume 91:Issue 6(2019)
• Page Start: 836
• Page End: 856
• Publication Date: 2019-08-18
• Subjects: Backward stochastic differential equation -- stochastic differential equation -- time-delayed coefficients -- time-advanced coefficients -- comparison theorem; 60H10; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2018.1551399
• Languages: English
• ISSNs: 1744-2508

Abstract

ABSTRACT: This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a sufficiently small Lipschitz constant, the existence and uniqueness of such BSDEs is obtained. As an adjoint process, a class of stochastic differential equations (SDEs) is introduced, whose coefficients also depend on the present, the past and the future of its solutions. The existence and uniqueness of such SDEs is proved for a sufficiently small time advance or a sufficiently small Lipschitz constant. A duality between such BSDEs and SDEs is established.